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Comment on "Experimental retrodiction of trajectories in double interferometer"Jul 12 2018Jul 15 2018A comment on a misleading statement contained in [Phys. Rev. A 97, 062115 (2018)]. v2: a typo corrected

The entire history of a photonJul 20 2017Using the most basic mathematical tools, I present the full analysis of the experiment decribed in [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)]. First, I confirm that the data presented therein are ... More

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategiesDec 17 2014May 05 2016Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown ... More

N-particle nonclassicality without N-particle correlationsDec 05 2011Jan 07 2013Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, ... More

Entanglement conditions involving intensity correlations of optical fields: the case of multi-port interferometryMar 01 2018Normalized quantum Stokes operators introduced in [Phys. Rev. A {\bf 95}, 042113 (2017)] enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers. For a given run of an experiment the ... More

Spectra in nested Mach-Zehnder interferometer experimentsJun 20 2018By the means of the standard quantum mechanics formalism I present an explicit derivation of the structure of power spectra in Danan {\em et al.} and Zhou {\em et al.} experiments with nested dynamically changing Mach-Zehnder interferometers. The analysis ... More

Theoretical Falsification of Leggett Conjecture for Two Qubits or One QuquatNov 18 2011Jan 08 2012Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments, and generalized ... More

Decoherence through Spin Chains: Toy ModelAug 22 2011Aug 29 2011The description of the dynamics of closed quantum systems, governed by the Schroedinger equation at first sight seems incompatible with the Lindblad equation describing open ones. By analyzing closed dynamics of a spin-1/2 chain we reconstruct exponential ... More

One-Qubit and Two-Qubit Codes in Noisy State TransferMay 04 2009Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects ... More

Subadditivity of logarithm of violation of geometric Bell inequalities for quditsFeb 20 2018Geometrical Bell Inequalities (GBIs) are the strongest known Bell inequalities for collections of qubits. However, their generalizations to other systems is not yet fully understood. We formulate GBIs for an arbitrary number $N$ of observers, each of ... More

Package of facts and theorems for efficiently generating entanglement criteria for many qubitsApr 12 2012Jun 25 2012We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds ... More

Criticism of "Asking Photons Where They Have Been"Jul 07 2014Oct 06 2016I stress that [PRL 111,240402(2013)] contains no result that need to be explained by so-called Two State Vector Formalism, and closely inspected data are in disagreement with claims of Danan, Farfurnik, Bar-Ad, and Vaidman

True Multipartite Entanglement Hardy TestMar 01 2013Dec 01 2014Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. ... More

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategiesDec 17 2014Oct 06 2016Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown ... More

Quadratic Entanglement Criteria for QutritsDec 22 2015Oct 17 2016The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation ... More

Quadratic Entanglement Criteria for QutritsDec 22 2015Oct 26 2016The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation ... More

Quantum Byzantine Agreement via Hardy correlations and entanglement swappingAug 07 2014We present a device-independent quantum scheme for the {\em Byzantine Generals} problem. The protocol is for three parties. Party $C$ is to send two identical one bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one bit ... More

Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradictionMay 07 2012Sep 21 2012Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell's inequalities is to assume existence of joint probability distribution for measurement results for all settings ... More

Hilbert-Schmidt distance and entanglement witnessingNov 15 2018Jan 23 2019Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance (HSD) between a given state and the set of separable ... More

Entanglement indicators for quantum optical fields: three-mode multiport beamsplitters EPR interference experimentsJan 10 2016Mar 01 2018We generalize a new approach to entanglement conditions for light of undefined photons numbers given in [Phys. Rev. A {\bf 95}, 042113 (2017)] for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one ... More

General mapping of multi-qudit entanglement conditions to non-separability indicators for quantum optical fieldsMar 08 2019We show that any multi-qudit entanglement witness leads to a non-separability indicator for quantum optical fields, which involves intensity correlation measurements and is useful for field states of undefined photon numbers. With the approach we get, ... More

Multipartite entanglement detection with minimal effortDec 18 2014Oct 06 2016Certifying entanglement of a multipartite state is generally considered as a demanding task. Since an $N$ qubit state is parametrized by $4^{N}-1$ real numbers, one might naively expect that the measurement effort of generic entanglement detection also ... More

Extending Bell inequalities to more partiesDec 21 2007May 06 2008We describe a method of extending Bell inequalities from $n$ to $n+1$ parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is non trivial in the sense that the inequalities produced ... More

Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR IdeasJul 28 2014Feb 18 2015Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode ... More

A classical-quantum hybrid oracle architecture for Boolean oracle identification in the noisy intermediate-scale quantum eraMay 14 2019Quantum algorithms have the potential to be very powerful. However, to exploit quantum parallelism, some quantum algorithms require an embedding of large classical data into quantum states. This embedding can cost a lot of resources, for instance by implementing ... More

Clearer visibility Hong-Ou-Mandel effect with correlation function based on rates rather than intensitiesJan 28 2016Oct 06 2016We test ideas put forward e.g in arXiv:1508.02368, which suggest that using rates in quantum optics can lead to better indicators of non-classicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered ... More

Clearer visibility Hong-Ou-Mandel effect with correlation function based on rates rather than intensitiesJan 28 2016Mar 07 2017We test ideas put forward e.g in arXiv:1508.02368, which suggest that using rates in quantum optics can lead to better indicators of non-classicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered ... More

Finding Traps in Non-linear Spin ArraysNov 18 2009Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear structure. While ... More

The build-up of mass in UV-selected sub-L* galaxies at z~2Feb 09 2011Broadband spectral energy distribution (SED) fitting is used to study a deep sample of UV-selected sub-L* galaxies at z~2. They are found to be less dusty than L* galaxies, and to contribute more mass to the cosmic mass budget at this epoch than is inferred ... More

Automatic continuity for isometry groupsDec 18 2013Jan 27 2014We present a general framework for automatic continuity results for groups of isometries of metric spaces. In particular, we prove automatic continuity property for the group of isometries of the Urysohn space and the Urysohn sphere, i.e. that any homomorphism ... More

On spectra and affine strict polynomial functorsDec 31 2015We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of $\infty$--affine strict ... More

Phase transition free regions in the Ising model via the Kac-Ward operatorJun 10 2013May 17 2015We investigate the spectral radius and operator norm of the Kac-Ward transition matrix for the Ising model on a general planar graph. We then use the obtained results to identify regions in the complex plane where the free energy density limits are analytic ... More

Atomic decompositions for Hardy spaces related to Schrödinger operatorsSep 16 2014Let L_U = -Delta+U be a Schr\"odinger operator on R^d, where U\in L^1_{loc}(R^d) is a non-negative potential and d\geq 3. The Hardy space H^1(L_U) is defined in terms of the maximal function for the semigroup K_{t,U} = exp(-t L_U), namely H^1(L_U) = {f\in ... More

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansionsFeb 17 2010Nov 26 2011For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a ... More

Complexity of Ramsey null setsMar 31 2010We show that the set of codes for Ramsey positive analytic sets is $\mathbf{\Sigma}^1_2$-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is $\mathbf{\Sigma}^1_1$-complete. ... More

Regularity and non-emptyness of linear systems in $\mathbb P^n$Feb 07 2008The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general position. To ... More

Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical systemApr 26 2019In this article we provide three new twist-deformed Newtonian Schwarzschild-(Anti-)de Sitter models. They are defined on the Lie-algebraically as well as on the canonically noncommutative space-times respectively. Particularly we find the corresponding ... More

Extreme amenability of abelian $L_0$ groupsJan 03 2012We show that for any abelian topological group $G$ and arbitrary diffused submeasure $\mu$, every continuous action of $L_0(\mu,G)$ on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and ... More

Linear systems in P^3 with low degrees and low multiplicitiesOct 12 2008We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the cases that have not been completed in a paper by E. Ballico and M.C. Brambilla. ... More

Casimir effect for tachyonic fieldsJul 04 2003Aug 29 2003In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use ... More

Algebraic approximation of analytic sets and mappingsDec 19 2007Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components of the sets ... More

The relation between the quantum games, communication complexity problems and Bell inequalitiesOct 22 2007We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding element in the ... More

Casimir effect in external magnetic fieldApr 13 2005Dec 19 2005In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we describe quantum ... More

The Ultraviolet-Far Infrared Energy Budget of the Gravitationally Lensed Lyman Break Galaxy MS1512-cB58Feb 12 2001A 2-hour service-mode SCUBA observation of the gravitationally-lensed Lyman break galaxy MS1512-cB58 resulted in a 3 sigma upper limit of 3.9 mJy at 850um. A comparison of this upper limit with values expected from rest-UV/optical measurements of extiction ... More

Remarks on normal basesOct 13 1997We prove that any Galois extension of commutative rings with normal basis and abelian Galois group of odd order has a self dual normal basis. Also we show that if S/R is an unramified extension of number rings with Galois group of odd order and $R$ is ... More

Quantum Information Processing with Continuous Variables and Atomic EnsemblesFeb 09 2011This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how ... More

On extremal positive maps acting between type I factorsDec 12 2008Dec 20 2008The paper is devoted to the problem of classification of extremal positive maps acting between $B(K)$ and $B(H)$ where $K$ and $H$ are Hilbert spaces. It is shown that every positive map with the property that $\rank \phi(P)\leq 1$ for any one-dimensional ... More

Rank properties of exposed positive mapsMar 17 2011May 10 2012Let $\cK$ and $\cH$ be finite dimensional Hilbert spaces and let $\fP$ denote the cone of all positive linear maps acting from $\fB(\cK)$ into $\fB(\cH)$. We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed point of $\fP$. ... More

Poincaré duality for Ext-groups between strict polynomial fucnctorsNov 09 2014We study relation between left and right adjoint functors to the precomposition functor. As a cosnequence we obtain various dualities in the Ext-groups in the category of strict polynomial functors.

Communication Complexity Reduction from Globally Uncorrelated StatesDec 11 2012Bell inequality violating entangled states are the working horse for many potential quantum information processing applications, including secret sharing, cryptographic key distribution and communication complexity reduction in distributed computing. ... More

SEDfit: Software for Spectral Energy Distribution Fitting of Photometric DataOct 01 2012This paper describes SEDfit, the earliest --- but continually upgraded --- software package for spectral energy distribution fitting (SED fitting) of high-redshift photometric data, and the only one to properly treat non-detections. The principles of ... More

Numerical investigations of the Schwinger model and selected quantum spin modelsMar 03 2013Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels ... More

N-enlarged Galilei Hopf algebra and its twist deformationsMay 02 2012The N-enlarged Galilei Hopf algebra is constructed. Its twist deformations are considered and the corresponding twisted space-times are derived.

Landau energy spectrum and quantum oscillator model for twisted N-enlarged Newton-Hooke space-timeDec 18 2014We derive the energy levels for oscillator model defined on the twisted N-enlarged Newton-Hooke space-time, i.e., we find time-dependent eigenvalues and corresponding time-dependent eigenstates. We also demonstrate that for a particular choice of deformation ... More

Reconfiguration in bounded bandwidth and treedepthMay 05 2014We show that several reconfiguration problems known to be PSPACE-complete remain so even when limited to graphs of bounded bandwidth. The essential step is noticing the similarity to very limited string rewriting systems, whose ability to directly simulate ... More

Sitnikov problem as a source of jetsAug 26 2011Sitnikov problem, consisting two close binaries and a third small body is considered, leading to a rapid ejection of the small body from the binaries. This mechanism is proposed as an explanation of jets in many astrophysical systems. Choosing appropriate ... More

Twisted acceleration-enlarged Newton-Hooke space-times and conservative force termsAug 09 2011There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that only in the case ... More

On the infimum convolution inequalities with improved constantsJan 24 2018The goal of the article is to improve constants in the infimum convolution inequalities (IC for short) which were introduced by R. Lata{\l}a and J.O. Wojtaszczyk. We show that the exponential distribution satisfies IC with constant $2$ but not with constant ... More

A comment on "Ab initio calculations of pressure-dependence of high-order elastic constants using finite deformations approach" by I. Mosyagin, A.V. Lugovskoy, O.M. Krasilnikov, Yu.Kh. Vekilov, S.I. Simak and I.A. AbrikosovDec 21 2017Recently, I. Mosyagin, A.V. Lugovskoy, O.M. Krasilnikov, Yu.Kh. Vekilov, S.I. Simak and I.A. Abrikosov in the paper: "Ab initio calculations of pressure-dependence of high-order elastic constants using finite deformations approach"[Computer Physics Communications ... More

Parallel Prefix Algorithms for the Registration of Arbitrarily Long Electron Micrograph SeriesDec 07 2017Recent advances in the technology of transmission electron microscopy have allowed for a more precise visualization of materials and physical processes, such as metal oxidation. Nevertheless, the quality of information is limited by the damage caused ... More

Classical capacity per unit cost for quantum channelsApr 21 2017Oct 06 2017In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication ... More

Monogamy of quantum entanglement in timeApr 13 2016In this paper we state a fundamental question about the structure of correlations in time and analyze temporal monogamy relations. We show that the nature of temporal correlations is inherently different from the spatial ones but in similarity to quantum ... More

Interpreting the 750 GeV diphoton excess in minimal extensions of Two-Higgs-Doublet modelsDec 23 2015Jun 07 2016It is shown that the 750 GeV diphoton excess can be explained in extensions of Two-Higgs-Doublet Models that do not involve large multiplicities of new electromagnetically charged states. The key observation is that at moderate and large $\tan\beta$ the ... More

A comment on the article "The Schwarz alternating method in solid mechanics" by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951]Dec 14 2017Recently, in the paper "The Schwarz alternating method in solid mechanics" by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951] the authors extended the well known Schwarz alternating method from linear ... More

Data adaptation in HANDY economy-ideology modelApr 08 2019The concept of mathematical modeling is widespread across almost all of the fields of contemporary science and engineering. Because of the existing necessity of predictions the behavior of natural phenomena, the researchers develop more and more complex ... More

The Zeeman effect for hydrogen atom in twist-deformed space-timeJan 20 2019In this article we find the Zeeman corrections for hydrogen atom in the case of twist-deformed space-time. Particularly, we derive the corresponding orbital and spin $\hat{g}$-factors as well as we notice, that the second one of them remains undeformed. ... More

The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebrasJan 16 2019In this article we discus the energy-momentum conservation principle for two-particle system in the case of canonically and Lie-algebraically twist-deformed Galilei Hopf algebra. Particularly, we provide consistent with the coproducts energy and momentum ... More

Error correction in quantum cryptography based on artificial neural networksOct 01 2018Apr 28 2019Intensive work on quantum computing has increased interest in quantum cryptography in recent years. Although this technique is characterized by a very high level of security, there are still challenges that limit the widespread use of quantum key distribution. ... More

Algorithm to Prove Formulas for the Expected Number of Questions in Mastermind GamesAug 11 2018We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors. For this purpose, ... More

Chaos synchronization of canonically and Lie-algebraically deformed Henon-Heiles systems by active controlJul 21 2018Recently, there has been provided two chaotic models based on the twist-deformation of classical Henon-Heiles system. First of them has been constructed on the well-known, canonical space-time noncommutativity, while the second one on the Lie-algebraically ... More

Forcing, games and families of closed setsOct 13 2009We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For definable ($\mathbf{\Pi}^1_1$ on $\mathbf{\Sigma}^1_1) $\sigma$-ideals we show ... More

A dichotomy for Borel functionsOct 08 2008The dichotomy discovered by Solecki in \cite{Sol} states that any Baire class 1 function is either $\sigma$-continuous or "includes" the Pawlikowski function $P$. The aim of this paper is to give an argument which is simpler than the original proof of ... More

A note on ccc forcingsSep 23 2008The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc $\sigma$-ideal I any I-positive Borel set contains modulo I an I-positive closed set?

The planar Ising model and total positivityJun 20 2016Dec 29 2016A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let $a_1,\dots,a_k,b_k,\dots,b_1$ be ... More

Affine strict polynomial functors and formalityNov 13 2014We introduce the notion of affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive characteristic. We ... More

Special homogeneous linear systems on Hirzebruch surfaces - algorithmic issuesNov 07 2009We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".

Reduction method for linear systems of plane curves with base fat pointsJun 28 2006In the paper we develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne Conjecture holds for systems with base points of equal multiplicity bounded ... More

Expected term bases for generic multivariate Hermite interpolationMar 30 2005The main goal of the paper is to find an effective estimation for the minimal number of generic points in $\mathbb K^2$ for which the basis for Hermite interpolation consists of the first $\ell$ terms (with respect to total degree ordering). As a result ... More

Special homogeneous linear systems on Hirzebruch surfacesJul 22 2009The Segre-Gimigliano-Harbourne-Hirschowitz Conjecture can be naturally formulated for Hirzebruch surfaces F_n. We show that this Conjecture holds for imposed base points of equal multiplicity bounded by 8.

A model of morphogen transport IINov 28 2014Apr 07 2015A model of morphogen transport consisting of two evolutionary PDEs of reaction-diffusion type and three ODEs posed on a rectangular domain is analysed. We prove that the problem is globally well-posed and that the corresponding solutions converge, as ... More

Approximation of maps into spheres by piecewise-regular maps of class C^kAug 21 2018Dec 13 2018The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More

Deuteron charge radius from the Lamb-shift measurement in muonic deuteriumDec 28 2018Mar 07 2019The deuteron charge radius is calculated from the measurement of the Lamb shift in muonic deuterium, taking into account the electron vacuum polarization correction to the nuclear-structure effects. This correction is unexpectedly large and gives a mean-square ... More

A comment on "The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals"Dec 13 2018Apr 30 2019Recently, Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S Schmidt, Nicki F Hinsche, Morten N Gjerding, Daniele Torelli, Peter M Larsen, Anders C Riis-Jensen, Jakob Gath, Karsten W Jacobsen, Jens Jrgen Mortensen, Thomas Olsen and ... More

Well-posedness and asymptotic behavior of a multidimensional model of morphogen transportDec 26 2011Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ... More

Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10Apr 08 2008In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least $m,...,m,m_0$, ... More

Galois theory for H-extensionsApr 29 2013We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria for subalgebras ... More

A model of morphogen transport in the presence of glypicans IIINov 28 2014Apr 07 2015We analyse a stationary problem for the two dimensional model of morphogen transport introduced by Hufnagel et al. The model consists of one linear elliptic PDE posed on $(-1,1)\times(0,h)$ which is coupled via a nonlinear boundary condition with a nonlinear ... More

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017May 13 2019We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More

Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-timesJan 10 2011The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke space-times are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time.

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 2Nov 12 2010In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the quantization of electrodynamics, ... More

Deformation of nonrelativistic space-time and forces noticed by noninertial observerJul 27 2010We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph], we recall ... More

Ellipsoids of U(3) modelNov 19 2009Nov 25 2009The Cartan model of SO(3)/SO(2) matrices is applied to reduce of rotational degrees of freedom on coadjoint orbits of u^*(3) Poisson algebra. The seven--dimensional Poisson algebra u_SO(3) obtained by SO(3) reduction of u^*(3) algebra is found and canonical ... More

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 1Oct 27 2010Nov 12 2010An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be consistently replaced ... More

Local approximation of the solutions of algebraic equationsMar 27 2008A method of local approximation of holomorphic solutions of algebraic equations is discussed

Quantum Wire as Open SystemNov 15 2007May 02 2008The faithful exchange of quantum information will soon become one of the challenges of the emerging quantum information technology. One of the possible solutions is to transfer a superposition through a chain of properly coupled spins. Such a system is ... More

Quasi-Quantum Model of PotentizationNov 23 2009Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during the decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist ... More

Investigation of astrophysical phenomena in short time scales with "Pi of the Sky" apparatusOct 07 2008In this thesis the data analysis designed by author for the "Pi of the Sky" experiment is presented. The data analysis consists of data reduction and specific algorithms for identification of short time scale astrophysical processes. The algorithms have ... More

Analysis of experimental uncertainties in the R-correlation measurement in the decay of free neutronsJun 29 2004Sep 07 2004The experiment aiming at the simultaneous determination of the two transversal polarisation components of electrons emitted in the decay of free, polarised neutrons is in progress at the Paul Scherrer Institute (Villigen, Switzerland). The non-zero value ... More

Approximation of sets defined by polynomials with holomorphic coefficientsDec 18 2007Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,...,a_s ... More